zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. (English) Zbl 1226.93014
Summary: We discuss the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader-follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. A rigorous proof is given by using the Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.
MSC:
93A14Decentralized systems
94C15Applications of graph theory to circuits and networks
93D05Lyapunov and other classical stabilities of control systems
References:
[1]Bhat, S. P.; Bernstein, D. S.: Finite-time stability of continuous autonomous systems, SIAM journal on control and optimization 38, No. 3, 751-766 (2000) · Zbl 0945.34039 · doi:10.1137/S0363012997321358
[2]Cortes, J.: Finite-time convergent gradient flows with applications to network consensus, Automatica 42, No. 11, 1993-2000 (2006)
[3]Dimarogonas, D.; Tsiotras, P.; Kyriakopoulos, K.: Leader–follower cooperative attitude control of multiple rigid bodies, Systems and control letters 58, No. 6, 429-435 (2009) · Zbl 1161.93002 · doi:10.1016/j.sysconle.2009.02.002
[4]Dong, W.; Farrell, A.: Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty, Automatica 45, No. 3, 706-710 (2009) · Zbl 1166.93302 · doi:10.1016/j.automatica.2008.09.015
[5]Fax, A.; Murray, R.: Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control 49, No. 9, 1453-1464 (2004)
[6]Hardy, G.; Littlewood, J.; Polya, G.: Inequalities, (1952) · Zbl 0047.05302
[7]Hong, Y.; Chen, G.; Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks, Automatica 44, No. 2, 846-850 (2008)
[8]Hong, Y.; Hu, J.; Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42, No. 7, 1177-1182 (2008) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013
[9]Hui, Q.; Haddad, W. M.; Bhat, S. P.: Finite-time semistability and consensus for nonlinear dynamical networks, IEEE transactions on automatic control 53, No. 8, 1887-1990 (2008)
[10]Khoo, S.; Xie, L.; Man, Z.: Robust finite-time consensus tracking algorithm for multirobot systems, IEEE/ASME transactions on mechatronics 14, No. 2, 219-228 (2009)
[11]Li, S.; Ding, S.; Li, Q.: Global set stabilisation of the spacecraft attitude using finite-time control technique, International journal of control 82, No. 5, 822-836 (2009) · Zbl 1165.93328 · doi:10.1080/00207170802342818
[12]Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control 51, No. 3, 410-420 (2006)
[13]Olfati-Saber, R.; Murray, R.: Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control 49, No. 9, 1520-1533 (2004)
[14]Qian, C.; Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE transactions on automatic control 46, No. 7, 1061-1079 (2001) · Zbl 1012.93053 · doi:10.1109/9.935058
[15]Ren, W.: Multi-vehicle consensus with a time-varying reference state, Systems and control letters 56, No. 7–8, 474-483 (2007) · Zbl 1157.90459 · doi:10.1016/j.sysconle.2007.01.002
[16]Ren, W.: On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control 53, No. 6, 1503-1509 (2008)
[17]Ren, W.; Atkins, E.: Distributed multi-vehicle coordinated control via local information exchange, International journal of robust and nonlinear control 17, No. 10–11, 1002-1033 (2007)
[18]Wang, X., & Hong, Y. (2008). Finite-time consensus for multi-agent networks with second-order agent dynamics. In Proceedings of IFAC world congress. Korea (pp. 15185–15190).
[19]Wang, L.; Xiao, F.: Finite-time consensus problems for networks of dynamic agents, IEEE transactions on automatic control 55, No. 4, 950-955 (2010)
[20]Xiao, F.; Wang, L.; Chen, J.; Gao, Y.: Finite-time formation control for multi-agent systems, Automatica 45, No. 11, 2605-2611 (2009) · Zbl 1180.93006 · doi:10.1016/j.automatica.2009.07.012